Results 81 to 90 of about 335 (183)
Girth in GF(q)$\textsf {GF}(q)$‐representable matroids
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3401-3407, November 2025.Abstract We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field GF(q)$\textsf {GF}(q)$ and any integer t$t$, every cosimple GF(q)$\textsf {GF}(q)$‐representable matroid with sufficiently large girth contains either M(Kt)$M(K_t)$ or M(Kt)∗$M(K_t)^*$ as a minor.
James Davies +4 more
wiley +1 more source
Factorization theorems for strong maps between matroids of arbitrary cardinality
Open Mathematics, 2016 In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
Mao Hua
doaj +1 more source
Equivariant Hilbert and Ehrhart series under translative group actions
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley +1 more source
A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)
IEEE Access, 2017 In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. First, a vector matroid is defined over F(z). Second, the full rank conditions of [sI - A|B](s ∈ p) are derived in terms of
Yupeng Yuan +4 more
doaj +1 more source
Discrete Mathematics, 1988 \textit{S. Poljak} and \textit{D. Turzik} [Discrete Math. 42, 119-123 (1982; Zbl 0491.05020)] call a geometric lattice L on the point set E sticky if for any two extensions \(L_ 1\) and \(L_ 2\) on \(E\cup X_ 1\) and \(E\cup X_ 2\), respectively, there exists a geometric lattice \(\tilde L\) on \(E\cup X_ 1\cup X_ 2\) with \(\tilde L\setminus X_ i=L_{3-
Achim Bachem, Walter Kern
openaire +2 more sources
On complete classes of valuated matroids [PDF]
TheoretiCSWe characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network.
Edin Husić +3 more
doaj +1 more source
Journal of Combinatorial Theory, Series B, 1978 AbstractIn this paper we define oriented matroids and develop their fundamental properties, which lead to generalizations of known results concerning directed graphs, convex polytopes, and linear programming. Duals and minors of oriented matroids are defined.
Robert G. Bland, Michel Las Vergnas
openaire +1 more source
CoRR, 2014 We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estimates for any solution method.
Király, FJ, Theran, L
openaire +3 more sources
Two-Stage Submodular Maximization Under Knapsack Problem
Tsinghua Science and TechnologyTwo-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization. In this paper, we consider knapsack constraint.
Zhicheng Liu +3 more
doaj +1 more source
Discrete Mathematics, 1995 This communication is an announcement of results for \(h\)-vectors of matroids which settle a conjecture of Stanley.
openaire +1 more source